CARPENTER'S 

AND 

JOINER'S 
HAND-BOOK. 


THE 

CAEPEUTEE'S  AND  JOINER'S 

HAND-BOOK: 


CONTAININCr 


A  COMPLETE  TREATISE  ON  FRAMING 
HIP  AND  VALLEY  ROOFS. 

TOGETHER  WITS 

MUCH  VALUABLE  INSTRUCTION  FOR  ALL  MECHANICS  AND 
AMATEURS,  USEFUL  RULES,  TABLES,  ETC., 
.  NEVER  BEFORE  PUBLISHED. 

REVISED  EDITION  WITH  ADDITIOm. 

BY 

PRACTICAL  ARCHITECT  AND  BUILDER, 
AUTHOR  OF 

«'THE  ART  OF  SAW-FILING." 


ILLUSTRATED  BY  FORTY-THREE  ENGRAVINGS. 


NEW  YORK  : 
JOHN  WILEY  &  SONS, 
15  AsTOR  Place. 
1882, 


Entered  according  to  Act  of  Congress,  ih  the  year  1863, 
By  H.  W.  holly, 
the  Clerk's  Office  of  the  District  Court  of  the  United  States  for 
the  District  of  Connecticut. 


PEEFACE. 


This  work  has  been  undertaken  by  tbe 
antlior  to  supply  a  want  long  felt  by  tlie 
trade :  that  is,  a  cheap  and  convenient 
"Pocket  Guide/'  containing  the  most  use- 
ful and  necessary  rules  for  the  carpenter. 

The  writer,  in  his  progress  "  through  the 
mill,"  has  often  felt  that  such  a  work  as  this 
would  have  been  of  great  value,  and  some 
one  principle  here  demonstrated  been  worth 
many  times  the  cost  of  the  book. 

It  is  believed,  therefore,  that  this  book  will 
commend  itself  to  those  interested,  for  the 
reason  that  it  is  cheap,  that  it  is  plain  and 
easily  understood,  and  that  it  is  useful. 


CONTENTS. 


ART. 


To  find  the  lengths  and  bevels  of  hip  and  common 

rafters   1 

To  find  the  lengths,  &c.,  of  the  jacks   2 

To  find  the  backing  of  the  hip  ,  3 

Position  of  the  hip-rafter   4 

"Where  to  take  the  length  of  rafters   5 

Difference  between  the  hip  and  valley  roof   6 

Hip  and  vaUey  combined   7 

Hip-roof  without  a  deck. .  .-^   8 

To  frame  a  concave  hip-roof   9 

An  easy  way  to  find  the  length,  &c.,  of  common 

rafters   10 

Scale  to  draw  roof  plans   11 

To  find  the  form  of  an  angle  bracket   12 

To  find  the  form  of  the  base  or  covering  to  a  cone. .  .  13 

To  find  the  shape  of  horizontal  covering  for  domes . . '  14 

To  divide  a  line  into  any  number  of  equal  parts   15 

To  find  the  mitre  joint  of  any  angle   16 

To  square  a  board  with  compasses   lY 

To  make  a  perfect  square  with  compasses   18 

To  find  the  centre  of  a  circle   19 

To  find  the  same  by  another  method   20 

Through  any  three  points  not  in  a  line,  to  draw  a 

circle   21 

Two  circles  being  given,  to  find  a  third  whose  area 

shall  equal  the  first  and  second   22 


6 


CONTENTS. 


ART. 

To  find  the  form  of  a  raking  crown  moulding   23 

To  lay  out  an  octagon  from  a  square   24 

To  draw  a  hexagon  from  a  circle   25 

To  describe  a  curve  by  a  set  triangle   26 

To  describe  a  curve  by  intersections   2t 

To  describe  an  elliptical  curve  by  intersection  of 

lines   28 

To  describe  the  parabolic  curve   29 

To  find  the  joints  for  splayed  work   30 

Stairs   31 

To  make  the  pitch-board   32 

To  lay  out  the  string   33 

To  file  the  fleam-tooth  saw   34 

To  dovetail  two  pieces  of  wood  on  four  sides   35 

To  splice  a  stick  without  shortening   36 

The  difference  between  large  and  small  files   3t 

Piling  wood  on  a  side-hill   38 

Another  mysterious  splice   39 

To  find  the  height  of  a  tree   40 

To  cut  bridging  to  fit   41 

Building  fence  over  a  hill   42 

To  draw  an  oval  with  a  string   43 

To  find  the  speed  of  shafting   44 

To  glue  mitre  and  butt  joints   45 

To  find  the  number  of  gallons  in  a  tank   46 

To  find  the  area  of  a  circle   47 

Capacity  of  wells  and  cisterns   48 

Weights  of  various  materials   49 


THE  CARPENTER'S  AND  JOINER'S 

HAND-BOOK- 


HIP  AND  YALLEY  EOOES. 

The  framing  of  liip  and  valley  roofs,  being 
of  a  different  nature  from  common  square 
rule  framing,  seems  to  be  understood  by 
very  few.  It  need  scarcely  be  said,  that  it  is 
very  desirable  tbat  this  important  part  of  a 
carpenter's  work  should  be  familiar  to 
every  one  who  expects  to  bes.rated  as  a  first- 
class  workman.  The  system  here  shown  is 
proved,  by  an  experience  of  several  years, 
to  be  perfectly  correct  and  practicable ;  and, 
as  it  is  simple  and  easily  understood,  it  is 
believed  to  be  the  best  in  use.  Care  has 
been  taken  to  extend  the  plates  so  as  to  de- 


THE  carpenter's 


monstrate  eacli  position  or  principle  by  it- 
self, so  that  the  inconvenience  and  confusion 
of  many  lines  and  letters  mixed  np  with 
each  other  may  be  avoided. 

Article  1. — To  find  the  lengths  andhevels 
of  hijp  and  common  rafters. 


'hetppp  (Fig.  1)  represent  the  face  of  the 
plates  of  the  building ;  d^  the  deck-frame : 


HAND-BOOK. 


9 


a  is  the  seat  of  the  hip-rafter;  5,  of  the 
jack ;  and  of  the  common  rafter.  Set  the 
rise  of  the  roof  from  the  ends  of  the  hip  and 
common  rafter  towards  e  square  from  a 
and  G  /  connect/*  and  then  the  line  from 
ftoe  will  be  tlie  length  of  the  hip  and  com- 
mon rafter,  and  the  angles  at  ^  ^  will  be  the 
down  bevels  of  the  same. 

2.  Tojmd  the  length  and  hevel  of  thejaclc- 
raftei's, 

h  (Fig.  1)  is  the  seat  of  a  jack-rafter.  Set 
the  length  of  the  hip  from  the  corner,  to 
the  line  on  the  face  of  the  deck-frame,  and 
join  it  to  the  point  at  g.  Extend  the  jack  h 
to  meet  this  line  at  h  /  then  from  i  to  h  will 
be  the  length  of  the  jack-rafter,  and  the 
angle  at  h  will  be  the  top  bevel  of  the  same. 

The  length  of  all  the  jacks  is  found  in  the 
same  way,  by  extending  them  to  meet  the 
line  A.  The  dovm  bevel  of  the  jacks  is  the 
same  as  that  of  the  common  rafter  at  e. 

3.  To  find  the  hacking  of  the  hip-rafter. 
At  any  point  on  the  seat  of  the  hip,  a  (Fig. 


10 


THE  carpenter's 


1),  draw  a  line  at  right  angles  to  extending 
to  the  face  of  the  plates  ^thh  j  upon  the 
points  where  the  lines  cross,  draw  the  half 
circle,  just  touching  the  Ymefej  connect  the 
point  aty,  where  the  half  circle  cuts  the  line 
a,  with  the  points  hh j  the  angle  formed at^' 
will  be  the  proper  backing  of  the  hip-rafter. 

It  is  not  worth  while  to  back  the  hip-raf- 
ter unless  the  roof  is  one-quarter  pitch  or 
.  more. 

4.  It  is  always  desirable  to  have  the  hip- 
rafters  on  a  mitre  line,  so  that  the  roof  will 
all  be  the  same  pitch ;  but  when  for  some 
reason  this  cannot  be  done,  the  same  rule  is 
employed,  but  the  jacks  on  each  side  of  the 
hip  are  different  lengths  and  bevels. 


HAND-BOOK. 


11 


Fig.  2. 

The  heavy  line  from  d  (Fig.  2),  shows  the 
seat  of  the  hip-rafter ;  a  and  the  jacks.  Set 
the  rise  of  the  roof  at  e  /  set  the  length  of 
the  hip  d  from  d  to/*  on  one  side  of  the 
deck,  and  from  6?  to  ^  on  the  other  side ;  ex- 
tend the  jack  J,  and  all  the  jacks  on  that 
side,  to  the  line  df^  for  the  length  and  top 
bevels ;  extend  the  jack  and  all  on  that 
side,  to  the  line  d  for  the  length  and  bevels 
on  that  side  of  the  hip.  The  down  bevels 
of  the  jacks  will  be  the  same  as  that  of  the 
common  rafters  on  the  same  side  of  the 
roof. 


12 


THE  carpenter's 


5.  The  lengths  of  hips,  jacks,  and  valley- 
rafters  should  be  taken  on  the  centre  line,  and 
the  thickness  or  half  thickness  allowed  for. 
(See  Fig.  3.) 


Fig.  3. 


6.  The  valley-roof  is  the  same  as  the  hip- 
roof inverted.  The  principle  of  construction 
is  the  same,  with  a  little  different  applica- 
tion. 


HAND-BOOK. 


13 


Fig.  4. 


Let  a  h  (Fig.  4)  represent  the  valley-rafter  ; 
j  j  are  corresponding  jack-rafters.  Set  the 
rise  of  the  roof  from  a  to  c  /  connect  h  and 
c :  from  5  to  ^  is  the  length  of  the  valley- 
rafter,  and  the  angle  at  g  the  bevel  of  the 
same ;  set  the  length  h  c  on  the  line  from 
extend  the  jack^  to  meet  the  line  b  d  at  e  ; 
then  from  etof  is  the  length  of  the  jack, 
and  the  angle  at  e  the  top  bevel  of  the  same. 

7.  When  the  hip  and  valley  are  combined^ 


14 


THE  carpenter's 


SO  that  one  end  of  the  jack  is  on  the  hip ^  and 
the  other  on  the  valley. 


Fig.  5. 


a  h  (Fig.  5)  is  the  hip,  and  c  d  the  valley- 
rafters.  Find  the  length  of  each  according 
to  the  previous  directions ;  find  the  lines  e 
and  f  as  before. 

Extend  the  jacks  j  j  to  the  line  e^  for  the 
top  bevel  on  the  hip :  extend  the  same  on 
the  other  end  to  the  line/*,  for  the  top  bevel 
on  the  valley ;  the  whole  lengths  of  the  jacks 


HAND-BOOK. 


15 


is  from  the  line/*  to  the  line  e.  If  the  hip 
and  valley  rafters  lie  parallel,  the  bevel  will 
be  the  same  on  each  end  of  the  jack. 

8.  In  framing  a  hip-roof  without  a  deck- 
ing or  observatory,  a  ridge-pole  is  nsed,  and 
of  such  a  length  as  to  bring  the  hip  on  a 
mitre  line ;  but  this  ridge-pole  must  be  cut 
half  its  thickness  longer  at  each  end,  or  the 
hip  will  be  thrown  out  of  place  and  the 
whole  job  be  disarranged. 


This  is  illustrated  by  the  figure.  Suppose 
the  building  to  be  16  by  20,  the  ridge  would 
require  to  be  four  feet  long ;  but  if  the  stick 
is  four  inches  thick,  for  instance,  then  it 


7 


i 

16  THE  carpenter's 

should  be  cut  four  feet  four  inches  long,  so  | 

that  the  centre  line  on  the  hip,     will  point  ' 

to  the  centre  of  the  end  of  the  ridge-pole,  \ 

J,  at  four  feet  long.  This  simple  fact  is  often  \ 

overlooked.  • 

9.  To  frame  a  concave  hip-roof, — (This  ] 

is  much  used  for  verandas,  balconies,  sum-  ; 

mer-houses,  &c.)  • 


P 


Fig.  T.  J 

To  find  the  curve  of  the  hip.  \  \ 

Let  a  (Fig.  7)  be  the  common  rafter  in  its  \ 
true  position,  the  line  h  being  level.  Draw  the  | 

i 

i 


HAiSTD-BOOK. 


17 


line  c  on  the  angle  the  hip-rafter  is  to  lie, 
generally  a  mitre  line ;  draw  the  small  lines 
0  0  0^  parallel  to  the  plate  The  more  of  these 
lines,  the  easier  to  trace  the  cnrve ;  continue 
the  lines  o  o  where  they  strike  the  line  c 
square  from  that  line  ;  set  the  distances  1,  2, 
3,  4,  &c.  (on  (2,  from  the  line  h)  on  the  line 
G  Gj  towards  at  right  angles  from  c  g  ; 
through  these  points,  2,  4,  6,  8,  e%c.,  trace 
the  curve,  which  will  give  the  form  of  the 
hip-rafter.* 

To  get  the  joints  of  the  jack-rafters,  take 
a  piece  of  plank  (Fig.  7),  the  thickness 
required,  wide  enough  to  cut  a  common 
rafter;  mark  out  the  common  rafter  the 
full  size.  Then  ni-et  the  len.g!:ths  and  bevels, 
the  same  as  a  straight  raftered  roof,  which 
this  will  be,  looking  down  upon  it  from 
above ;  then  lay  out  your  joints  from  the 
top  edge  of  the  plank,  as/y  /  cut  these  joints 
first,  saw  out  the  curves  afterwards,  and  you 
will  have  your  jacks  all  ready  to  put  up. 
Cut  one  jack  of  each  length  by  this  method, 

*  Do  not  attempt  to  £ret  the  form  of  a  curved  hip-rafter,  or  an- 
jrle  bracket,  by  sweeping  it  from  a  centre.  It  cannot  be  done, 
for  it  is  a  part  of  an  ellipse  and  not  a  part  of  circle.  It  can  only 
be  found  by  tracing  it  through  the  points  as  shown. 


18 


THE  carpenter's 


then  nse  this  for  a  pattern  for  the  others,  so 
as  not  to  waste  stuff.  It  will  be  seen  that 
the  down  bevel  is  different  on  each  jack, 
from  the  curve^  but  the  same  from  a  straight 
line,  from  point  to  point  of  a  whole  rafter.* 

10.  A  quick  and  easy  way  to  find  the 
lengths  and  hevels  of  common  rafters. 

Suppose  a  building  is  40  feet  wide,  and 
the  roof  is  to  rise  seven  feet.  Place  your 
steel  square  on  a  board  (Fig.  8),  twenty 
inches  from  the  corner  one  way,  and  seven 
inches  the  other.  The  angle  at  c  will  be 
the  bevel  of  the  upper  end,  and  the  angle 
at  d^  the  bevel  of  the  lower  end  of  the  rafter. 


Fig.  S. 


11.  The  length  of  the  rafter  will  be  from 
a  to  5,  on  the  edge  of  the  board.  Always  buy 
a  square  with  the  inches  on  one  side  divided 


*  Of  courpe  a  convex  roof  is  framed  on  the  same  plan.  The 
same  thing  precisely,  reversed. 


hand-book:. 


19 


into  twelfths,  then  you  have  a  convenient 
scale  always  at  hand  for  such  work  as  this. 
The  twenty  inches  shows  the  twenty  feet, 
half  the  width  of  the  building ;  the  seven 
inches,  the  seven  foot  rise.  Now  the  distance 
from  a  to  5,  on  the  edge  of  the  board,  is 
twenty-one  inches,  two-twelfths,  and  one- 
quarter  of  a  twelfth,  therefore  this  rafter  will 
be  21  feet  2|-  inches  long. 

12.  To  find  the  form  of  an  angle  hracket 
for  a  cornice. 


Let  a  (Fig.  9)  be  the  common  bracket ; 
draw  the  parallel  lines  o  o  o^io  meet  the 


20 


THE  carpenter's 


mitre  line  c ;  square  tip  on  eacli  line  at 
and  set  the  distances  1,  2,  3,  4,  (fee,  on  the 
common  bracket,  from  the  line  on  the 
small  lines  from  c  ;  through  these  points,  2, 
4,  6,  &c.,  trace  the  form  of  the  bracket. 
This  is  the  same  principle  illustrated  at  Fig. 
7  and  Fig.  20. 

13.  To  find  the  form  of  a  hase  or  covering 
for  a  cone. 


i^lg.  10. 


Ler  a  (Fig.  10)  be  the  width  of  the  base 
to  the  cone.  Draw  the  line  h  through  the 
centre  of  the  cone ;  extend  the  line  of  the 
side  c  till  it  meets  the  line  &  at  <^  /  on  6?  for 
a  centre,  with  1  and  2  for  a  radius,  describe 


HAND-BOOK. 


21 


which  will  be  the  shape  of  the  base  re- 
quired; /*will  be  the  joint  required  for  the 
same. 

14.  To  find  the  shape  of  horizontal  cover- 
ing for  circular  domes. 

The  principle  is  the  same  as  that  employed 
at  Fig.  10,  supposing  the  surface  of  the  dome 
to  be  composed  of  many  plane  surfaces. 
Therefore,  the  narrower  the  pieces  are,  the 
more  accurately  they  will  fit  the  dome. 


Fig.  11. 


Draw  the  line  a  through  the  centre  of  the 
dome  (Fig.  11);  divide  the  height  from  h  to 


22 


THE  carpenter's 


G  into  as  many  parts  as  there  are  to  be 
courses  of  boards,  or  tin.  Through  1  and  2 
draw  a  line  meeting  the  centre  line  at  d  j 
that  point  will  be  the  centre  for  sweeping 
the  edges  of  the  board  g.  Through  2  and 
3,  draw  the  line  meeting  the  centre  line  at 
e ;  that  will  be  the  centre  for  sweeping  the 
edges  of  the  board  and  so  on  for  the  other 
courses. 

15.  To  divide  a  line  into  any  nuinber  of 
equal  jparts. 


Fig.  12. 


Let  a  h  (Fig.  12)  be  the  given  line.  Draw 
the  line  a  at  any  convenient  angle,  to  ah  ; 
set  the  dividers  any  distance,  as  from  1  to  2, 
and  run  off  on  a  as  many  points  as  you 
wish  to  divide  the  line  a  l  into  ;  say  Y  parts ; 


HAND-BOOK. 


23 


connect  the  point  Y  with  5,  and  draw  the 
lines  at  6,  5^  4,  (fee,  parallel  to  the  line  7 
J,  and  the  line  a  h  will  be  divided  as  desired. 
16.  To  find  the  mitre  joint  of  any  angle. 


Fig.  13. 


Let  a  and  h  (Fig.  13)  be  the  given  angles ; 
set  off  from  the  points  of  the  angles  equals 
distances  each  way,  and  from  those  points 
sweep  the  parts  of  circles,  as  shown  in  the 
figure.  Then  a  line  from  the  point  of  the 
angle  through  where  the  circles  cross  each 
other,  will  be  the  mitre  line. 


24:  THE  CARPENTEe's 

17.  To  square  a  loard  with  compasses. 


1 


Fig.  14. 


Let  a  (Fig,  14)  be  the  board,  and  h  the 
point  from  which  fo  square.  Set  the  com- 
passes from  the  point  h  any  distance  less 
than  the  middle  of  tlie  board,  in  the  direc- 
tion of  G,  Upon  G  for  a  centre  sweep  the 
circle,  as  shown.  Then  draw  a  straight  line 
from  where  the  circle  tenches  the  lower  edge 
of  the  board,  through  the  centre  c^  cutting 
the  circle  at  d.    Then  a  line  from  h  through 

will  be  perfectly  square  from  the  lower 
edge  of  the  board.  This  is  a  very  useful 
problem,  and  will  be  found  valuable  for  lay- 
ing out  walks  and  foundations,  by  using  a 
line  or  long  rod  in  place  of  compasses. 


HAND-BOOK.  25 

18.  To  make  a  j^erfect  sq;uaTe  with  a  pair 
of  compasses. 


Fig.  15. 

Let  a  l  (Fig.  15)  be  the  lengtli  of  a 
side  of  the  proposed  square  ;  upon  a  and  5, 
with  the  whole  length  for  radius,  sweep 
the  parts  of  circles  a  d  and  5  c.  Find  half 
the  distance  from  a  to  e  2it  f ;  then  upon  e 
for  a  centre  sweep  the  circle  cutting/l  Draw 
the  lines  from  a  and  through  where  the 
circles  intersect  at  c  and  d ;  connect  them 
at  the  top  and  it  will,  form  a  perfect  square. 


3 


26  THE  carpenter's 

19.  To  find  the  centre  of  a  circle. 


Fig.  16. 

Upon  two  points  nearly  opposite  each 
other,  as  J  (Fig.  16),  draw  the  two  parts 
of  circles,  cutting  each  other  at  c  d ;  repeat 
the  same  at  the  points  e  f ;  draw  the  two 
straight  lines  intersecting  at  which  will 
be  the  centre  required. 


HAND-BOOK. 

20.  Another  method. 


27 


Fig.  17. 


Lay  a  square  upon  the  circle  (Fig.  17), 
with  the  corner  just  touching  the  outer  edge 
of  the  circle.  Draw  the  line  a  i  across  the 
circle  where  the  outside  edges  of  the  square 
touch  it.  Then  half  the  length  of  the  line  a 
1)  will  be  the  centre  required.  No  matter 
what  is  the  position  of  the  square,  if  the  cor- 
ner touches  the  outside  of  the  circle,  the  re- 
sult is  the  same,  as  shown  by  the  dotted 
lines. 


28  THE  carpenter's 

21.  Through  any  three  points  not  in  a  line^ 
to  draw  a  circle. 


Fig.  18. 


Let  a  h  c  (Fig  18)  be  the  given  points.  i 

Upon  each  of  these  points  sweep  the  parts  | 

of  circles,  cutting  each  otlier,  as  shown  in  the  \ 

figure ;  draw  the  straight  lines  d  d^  and  where  * 
they  intersect  each  other  will  be  the  centre 

required.    This  method  may  be  employed  ^ 

to  find  the  centre  of  a  circle  w^here  but  part  ; 
of  the  circle  is  given,  as  from  aio  c. 

22.  Two  circles  leing  given^  to  find  a  third  I 

whose  surface  or  area  shall  equal  the  first  j 

and  second.  ■ 


HAND-BOOK. 


29 


rig.  19. 


Let  a  and  h  (Fig.  19)  be  tlie  given  circles. 
Place  tlie  diameter  of  each  at  right  angles  to 
the  other  as  at  3,  connect  the  ends  at  c  and 
then  c  d  will  be  the  diameter  of  the 
circle  required. 

23.  To  find  the  form  of  a  raking  crown 
moulding. 


Fig.  20. 


so 


THE  carpenter's 


m  (Fig.  20)  is  tlie  form  of  the  level  crown 
moulding;  r  c  \%  the  pitch  of  the  roof. 
Draw  the  line  Z,  which  shows  the  thickness 
of  the  moulding.  Draw  the  lines  o  o  par- 
allel to  the  rake.  Where  these  lines  strike 
the  face  of  the  level  moulding,  draw  the  hor- 
izontal lines  1,  2,  3,  &c.  Draw  the  line  f 
square  from  the  rake :  set  the  same  distances 
from  this  line  that  you  find  on  the  level 
moulding  1,  2,  3,  &c.  Trace  the  curve 
through  these  points  1,  2,  3,  &c.,  and  you 
have  the  form  of  the  raking  moulding. 

Hold  the  raking  moulding  in  the  mitre 
I)ox,  on  the  same  pitch  that  it  is  on  the  roof, 
the  box  being  level,  and  cut  the  mitre  in 
that  position. 

24.  To  mahe  an  octagon^  or  eight-sided 
figure^  from  a  square. 


HAND-BOOK. 


31 


F?g.  21. 

Let  Fig.  2  i  be  the  square ;  find  the  centre 
a  J  set  the  compasses  from  the  corner  J,  to 
a  ;  describe  the  circle  cutting  the  outside  line 
at  c  and  6?;  repeat  the  same  at  each  corner, 
and  draw  lines  c  f  h  and  ij.  These 
lines  will  form  the  octagon  desired 

25,  To  draw  a  hexagon  or  six-sided  Jtg- 
nre  on  a  circle. 

Each  side  of  a  hexao^on  drawn  within  a 
circle  is  just  half  the  diameter  of  that  circle. 
Therefore  in  describing  the  hexagon  (Fig.  22), 
first  sweep  the  circle ;  then  without  altering 
the  compasses,  set  off  from  cc  to  5,  from  h  to  c^ 
and  so  on.    Join  all  these  points,       J,  c^ 


32  THE  carpenter's 


Fig.  22. 


&C.5  and  you  tiave  an  exact  hexagon.  Join 
J,  andy,  and  yon  have  an  equilateral  tri- 
angle ;  join  and  the  centre,  ^nd  you 
have  another  triangle,  just  one-sixth  of  the 
hexagon  described. 

26.  To  describe  a  curve  hy  a  set  triangle. 


Fig.  23. 


Let  a  I  (Fig.  23)  be  the  length,  and  c  d 
the  height  of  the  curve  desired ;  drive  two 


HAND-BOOK. 


33 


pins  or  awls  at  e  and  e  ;  take  two  strips  s 
tack  them  together  at  bring  the  edges  out 
to  the  pins  at  e ;  tack  on  the  brace  to 
keep  them  in  place ;  hold  a  pencil  at  the 
point  d  J  then  move  the  point  6?,  towards 
both  ways,  keeping  the  strips  hard  against 
the  pins  at  and  the  pencil  will  describe 
the  curve,  which  is  a  portion  of  an  exact  cir- 
cle. If  the  strips  are  placed  at  right  angles, 
the  curve  will  be  a  half  circle. 

This  is  a  quick  and  convenient  way  to  get 
the  form  of  flat  centres,  for  brick  arches, 
window  and  door  heads,  &c. 


Fig.  24. 


27.  Fig.  24  shows  the  method  of  forming 

a  curve  by  intersection  of  lines.    If  the 

points  1,  2,  3,  &c.,  are  equal  on  both  sides, 

the  curve  will  be  part  of  a  circle. 
3- 


34c 


THE  carpenter's 


28.  Fig.  25  sliows  how  to  form  an  ellipti- 
cal curve  by  intersections.  Divide  the  dis- 
tance a  by  into  as  many  points  as  from  i  to 


Fig.  25. 


and  proceed  as  in  Fig.  24.  The  closer  the 
points  1,  2,  3,  &c.,  are  together,  the  more 
accurate  and  clearly  defined  will  be  the 
curve,  as  at  d. 

29.  Fig.  26  shows  the  jparaholiG  curve. 


Fig.  26. 


HAND-BOOK.  35 

This  is  the  form  of  the  curve  of  the  Gothic 
arch  or  groin. 

30.  To  find  the  joints  for  splayed  work^ 
such  as  hoppers^  trays^  &g. 


Fig.  2T. 


Take  a  separate  piece  of  stuff  to  find  the 
joints  for  the  hopper,  Fig.  27.  Strike  the 
bevel  /    the  bevel  of  the  hopper,  on  the 


1 

c 

1 

/ 

36 


THE  carpenter's 


end  of  the  piece  (Fig.  28) ;  ran  tlie  gange- 
mark  c  fromy ;  then  square  on  the  edge  from 

or  where  you  want  the  outside  joint,  to  5/ 
then  square  down  from  5  to  the  gauge-mark 
c  /  strike  the  bevel  of  the  work  f  from  i 
to  through  the  point  at  e.  From  a  to  d 
will  be  the  joint,  the  inside  corner  the 
longest.  If  a  mitre  joint  is  wanted,  set  the 
thickness  of  the  stuff,  measuring  onfg^  from 
d  to  h  ;  the  line  a  h  will  be  the  mitre  joint. 

31.  Stair s,"^ — It  is  not  practicable  in  a 
work  of  this  size  to  go  into  all  the  details  of 
stair-building,  hand-railing,  &c.,  but  a  few 
leading  ideas  on  plain  stairs  may  be  intro- 
duced. 

First,  measure  the  height  of  the  story  from 
the  top  of  one  floor  to  the  top  of  the  next ; 
also  the  run  or  distance  horizontally  from 
the  landing  to  where  the  first  riser  is  placed. 

*  For  a  thorough  treatise  on  stair-building  in  all  its  de- 
tails, and  many  other  subjects  of  interest  to  the  builder, 
I  would  recommend  "  The  American  House  Carpenter," 
by  E.  G.  Hatfield,  New  York. 


HAND-BOOK. 


37 


Suppose  the  height  to  be  10  ft.  4  in.,  or  124: 
inches.  As  the  rise  to  be  easy  should  not 
be  over  8  inches,  divide  124  by  8  to  get  the 
number  of  risers :  result,  15^.  As  it  does 
not  come  out  even,  we  must  make  the  num- 
ber of  risers  16,  and  divide  it  into  124  inches 
for  the  width  of  the  risers:  result,  7f,  the 
width  of  the  risers.  If  there  is  plenty  of 
room  for  the  run,  the  steps  should  be  made 
10  inches  wide  besides  the  nosing  or  projec- 
tion ;  but  suppose  the  run  to  be  limited,  on 
account  of  a  door  or  something  else,  to  10 
ft.  5  in.,  or  125  inches :  divide  the  distance 
in  inches  by  the  number  of  steps,  which  is 
one  less  than  the  number  of  risers,  because 
the  upper  floor  forms  a  step  for  the  last  riser. 
Divide  125  by  15,  which  gives  8^  or  8^^^ 
inches,  the  neat  width  of  the  step,  which 
with  the  nosing,  will  mseke  about  a  9J  step. 
32.  To  make  a  pitch-hoard. 
4 


38 


THE  carpenter's 


Fig.  29. 


Take  a  piece  of  tliin  clear  stuff  (Fig.  29), 
and  lay  the  square  on  tlie  face  edge,  as 
shown  in  the  figure,  and  mark  out  the  pitch- 
board  j9  with  a  sharp  knife. 

33.  To  lay  out  the  string, 

JSTail  a  piece  across  the  longest  edge  of  the 
pitch-board,  as  at  5,  so  as  to  hold  it  up  to 
the  string  more  conveniently.  Then  begin 
at  the  bottom,  sliding  the  pitch-board  along 
the  upper  edge  of  the  string,  and  marking  it 
out,  as  shown  at  Fig.  30. 


p 

Fig.  SO. 


IIAND-BOOK.  39 

The  bottom  riser  must  scribe  down  to  the 
.  thickness  of  the  step  narrower  than  the 
"Others. 

34.  To  file  the  fleam-tooth  saw. 


Fig.  31. 


Fig.  31  shows  the  manner  of  filing  the 
fleam,  or  lancet  toothed  saw.  a  shows  the 
form  of  the  teeth,  full  size ;  and  5,  the  position 
of  holding  the  saw.  The  saw  is  held  flat  on 
the  bench,  and  one  side  is  finished  before  it 
is  turned  over.  No  setting  is  needed,  and 
the  plate  should  be  thin  and  of  the  very 
best  quality  and  temper. 


40 


THE  carpenter's 


These  saws  cut  at  an  astonisliing  rate,  cut- 
ting equally  botli  ways,  and  cut  as  smooth 
as  if  the  work  were  finished  with  the  keenest 
plane. 

35.  To  dovetail  two  pieces  of  wood  show- 
ing the  dovetail  on  four  sides. 


Fig.  82. 


a  (Fig.  32)  shows  two  blocks  joined  to- 
gether with  a  dovetail  on  four  sides.  This 


HAND-BOOK. 


looks  at  first  like  an  impossibility,  but  h 

shows  it  to  be  a  very  simple  matter.  This 

is  not  of  miicli  practical  nse  except  as  a 

pnzzle.  I  liave  seen  one  of  these  at  a  fair 
J. 

attract  great  attention;  nobody  could  tell 
how  it  was  done.  The  two  pieces  should  be 
of  different  colored  wood  and  glued  to- 
gether. 

36.  To  mend  or  splice  a  Ijrolien  stick  loitJi- 
ont  mahing  it  any  shorter  or  using  any  new 
stuff, 

A  vessel  at  sea  had  the  misfortune  to 
break  a  mast,  and  there  was  no  timber  of 
any  kind  to  mend  it.  The  carpenter  ingeni- 
ously overcame  the  difficulty,  without  short- 
ening the  mast. 


1 

—I.  - 

z 

\ 

} 

Fig.  33. 

4* 


42 


THE  carpenter's 


e  ail  (Fig.  33)  sliows  where  the  mast  was 
broken.  Out  the  piece  a  say  three  feet 
long,  and  the  piece  c  six  feet  long,  half 
way  through  the  stick.  Take  ont  these  two 
pieces,  keeping  the  two  broken  ends  to- 
gether, turn  them  end  for  end,  and  put  them 
back  in  place,  as  shown  at  2. 

This  arrangement  not  only  brought  the 
vessel  safe  home,  but  was  considered  by  the 
owners  good  for  another  voyage. 

By  putting  hoops  around  each  joint,  the 
stick  would  be  about  as  strong  as  ever. 

37.  Is  there  any  difference  in  the  angle 
of  a  large  or  small  three-cornered  fZe  ? 

Certainly  not :  for  the  file  is  an  equilateral 
triangle,  equal  on  all  sides. 


Fig.  34. 


Fig.  34  proves  this.       is  a  file  measuring 


HAND-BOOK. 


43 


one  incli  on  all  sides ;  cut  off  J,  making  a 
file  i  inch,  on  the  sides,  it  will  readily  be  seen 
that  the  angle  is  exactly  the  same. 

Simple  as  this  fact  is,  it  is  unknown  to 
many. 

38.  Does  a  pile  of  wood  on  a  side  hill 
2>iled  perpendicularly^  eight  feet  long ^ four 
wide^  and  four  high^  contain  a  cord  f 

It  does  not. 

 8 

4 


F4g.  35. 

To  illustrate,  let  us  make  a  frame  (Fig. 
35)  just  4  by  8  in  the  clear.  When  this 
frame  stands  level  it  will  hold  just  a  cord. 


4:4 


THE  carpenter's 


Fig.  86. 


Place  tliis  frame  on  a  side  hill,  so  as  to  give 
it  the  position  in  Fig.  it  will  be  seen  that 
the  8  ft.  sides  are  brought  nearer  together, 
thus  lessening  its  capacity.  Continue  to  in- 
crease the  steepness  of  the  ground,  as  at  Fig. 
37,  or  more,  the  8  ft.  sides  would  finally 


HAND-BOOK. 


45 


come  together,  and  the  frame  contain  noth- 
ing at  all.  It  therefore  becomes  careful 
buyers  of  wood  to  consider  where  it  is  piled. 

39.  Another  mysterious  splice  or  puzzle 
joint,  on  the  same  principle  as  Fig.  32,  is 
shown  at  Fig.  38. 


Fig.  38. 


The  pieces  slide  together  diagonally,  as 
will  be  seen  by  Fig.  39.    This  shows  one 

Fig.  39. 


piece  and  the  way  it  is  cut  ont.    The  other 


46 


THE  carpenter's 


piece  is  cut  just  like  it,  only  it  must^a^V 
with  this  one. 

40.  To  find  the  height  of  a  tree. 


'I. 


\   Fig.  40. 


Suppose  you  want  a  stick  of  timber  30  feet 
long,  and  want  to  know  if  a  certain  tree  will 
make  it.  Measure  o£E  from  tlie  tree  (Fig.  40), 


HAND-BOOK. 


47 


thirty  feet  on  a  level  from  where  you  will 
cut  it  down,  ten  feet  back  at  set  up 
your  ten-foot  pole;  let  some  one  hold  it 
plumb  while  you  put  your  eye  at  e.  Then 
looking  over  the  top  of  the  pole  where 
the  eye  strikes  the  tree  at  will  be  30  feet 
from     if  the  pole  is  held  right. 

41.  To  cut  bridging  to  fit  exactly  the  first 
time. 


Let  etc.  (Fig.  41),  show  the  floor  beams, 
being  different  distances  apart.  Snap  a  line 
at  G  to  nail  the  bridging  by,  then  snap  an- 
other line  at  &,  the  distance  from  the 


48 


THE  CAKPENTER'& 


deptli  of  the  timber.  Lay  a  piece  of  bridg- 
ing stuff  (d)  on  the  timber,  and  mark  it  on 
the  under  side  by  the  timber  as  shown  by 
the  short  dotted  lines ;  saw  it  correctly,  and 
it  will  fit  exactly  when  in  place,  no  matter 
what  distance  apart  the  timber  is. 

42.  Does  it  take  more  pickets  to  htdld  a 
fence  over  a  hill  than  on  a  level  f 

This  question  has  often  been  asked,  and 
even  published  in  some  newspapers,  and  an- 
swered in  the  aflirmative  by  some  very  wise 
persons.  At  first  thought  it  would  appear 
that  it  would  take  more,  but  a  look  at  Fig.  42 
settles  the  question  at  once.  In  building  a 
fence  level  from  A  to  i?,  we  have  a  certain 
number  of  pickets  as  shown.  Now  suppose 
the  curved  lines  ^  ^  to  represent  the  rise  and 
fall  of  a  hill,  we  see,  if  the  pickets  from  A  to 
'  B  are  carried  up  by  the  dotted  lines,  they 
make  the  same  fence  over  the  hill  and  are  no 
farther  apart  than  on  the  level. 


HAKB-BOOK, 


49 


Fig.  4:2. 


> 


>  


A. 


w  w 


3 


:^__r£:±i::> 


50  THE  CAKPEKTEE'S 

43.  To  draw  a  regular  oval  with  a  string. 


Fig.  43. 


b 


Drive  two  pins  at  a  a  (Fig.  43),  as  far 
apart  as  half  the  length  you  want  the  oval ; 
put  the  string  around  the  pins,  and  tie  at  5, 
the  same  distance  from  a  as  from  a  to  a. 
Place  your  pencil  at  J,  and  move  it  along, 
keeping  it  taut ;  in  the  direction  of  a^  both 
ways  letting  the  string  slide  on  the  pins,  and 
not  on  the  pencil. 

A  regular  oval  is  a  cylinder  cut  at  an 
angle  of  forty-five  degrees.  Savv^  a  piece 
of  lead  pipe  in  a  mitre  box,  and  the  end 
is  a  regular  oval. 

44.  To  find  the  sjpeed  of  shafting  and 
pulleys. 


HAKD-BOOK. 


51 


Rule,  Multiply  tlie  revolutions  of  the 
main  or  driving  shaft  by  the  diameter  of 
the  driving  pulley,  and  divide  by  the  diam- 
eter of  the  driven  pulley. 

Example.  Suppose  the  main  line  of  shaft- 
ing through  the  shop  is  running  at  the  rate 
of  one  hundred  turns  a  minute.  Tou  wish 
to  get  a  speed  on  another  shaft  of  400 
revolutions.  Put  a  24  inch  pulley  on  the 
main  line,  and  belt  on  to  a  6  inch  pulley, 
thus  100  X  24  =  2,400  6  =  400.  l^ow 
from  this  shaft  running  400,  you  want  a 
farther  speed  of  1,500.  Put  a  15  in.  pulley 
and  belt  on  to  a  4  in.  Thus  400  x  15  = 
6,000  -T-  4  1,500.  On  this  shaft  running 
1,500,  put  a  9  in.  pulley  and  belt  on  to  a  3  in., 
and  you  have  1,500  x  9  =  13,500  -f-  3= 
4,500.  Forty-five  hundred  revolutions  a  min- 
ute. To  save  pulleys  and  belts,  you  could  put 
a  48  in.  pulley  on  your  main  shaft,  and  belt- 
ing on  to  a  3  in.  pulley,  you  would  get  100  x 
48  =  4,800  3  =  1,600.  Sixteen  hundred 
revolutions  with  only  one  belt. 


52 


THE  carpenter's 


This  rule,  like  all  good  rules,  will  work 
both  ways.  For  instance,  take  the  first  ex- 
ample :  our  last  shaft  was  running  at  forty- 
five  hundred ;  now  call  this  the  driving- 
shaft. 

4,500  X  3  =  13,500  -   9  =  1,500 
1,500  X  4t=   6,000  -5-  15  =  400 
400  X  6  =   2,400  ~  24  =  100 
bringing  us  back  to  our  original  one  hun- 
dred revolutions. 

45.  To  glue  mitre  and  hutt  joints. 

It  is  considered  a  valuable  secret  by  some 
that  if  mitre  and  butt  joints  are  chalked  be- 
fore gluing  they  will  hold  as  well  as  any 
other  joint.    It  is  worth  trying. 

46.  To  find  the  number  of  gallons  in  a 
tank  or  hoXj  multiply  the  number  of  cubic 

.  feet  in  the  tank  by  7f . 


HAND-BOOK. 


53 


How  many  gallons  in  a  tank  8  feet  long, 
4  feet  wide,  and  3  feet  liigh  ? 
8 

4^ 

32 
3 

96  cubic  feet. 


672 
72 


Ans.    744  gallons. 


54  THE  carpenter's 

47.  To  find  the  area  or  number  of  square 
feet  in  a  cirele. 

Three-quarters  of  the  square  of  the  diam' 
eter  will  give  the  area. 

What  is  the  area  of  a  circle  &fL  in  diam' 
eter  ? 

6 
6 

36 

3 
4 

Ans,    27  feet. 

For  large  circles,  or  where  greater  accu- 
racy is  required,  multiply  the  square  of  the 
diameter  by  the  decimal  .785. 


\ 


HAKD-BOOK.  55 

48.  Capacity  of  wells  and  cisterns. 
One  foot  in  depth  of  a  cistern  : 
3  feet  in  diameter  contains    55^  gallons. 


3i  u  u  a        /jrg  a 

4  "  "  "       98  " 

^  u  u  u  1241  " 

5  "  "  153i  " 
51  feet  in  diameter  contains  185^  " 

6  "  220|  " 

7  "  "  300i  " 

8  "  "  "  392i  " 

9  "  "  497  " 

10  "  "  "  6131  a 


A  gallon  is  required  by  law  to  contain 
eight  pounds  of  pure  water. 


56  THE  CARPEl^TEK'S 


49.  Weights  of 

vdvious  materials  : 

Lbs.  in  a 

cubic  foot. 

Cast-iron  - 

-      -      -      -  460 

Cast-lead 

-      -      -      -  Y09 

Gold  - 

-  1,210 

Platina  - 

-      -      -  1,345 

Steel  - 

-  488 

Pewter  - 

-  453 

Brass 

-  506 

Copper  - 

-  549 

Granite 

-    .  -      -      -  166 

Marble  - 

-  170 

Blue  stone 

-  160 

Pnmice-stone 

-  56 

Glass 

-  160 

Chalk  -  - 

-  150 

Brick 

-      -  103 

Brickwork  laid 

-      -      -  95 

Clean  sand 

-  100 

Beech-wood  - 

-  40 

Ash  . 

45 

Birch  - 

-      -      -      -  45 

Cedar 

-      -  28 

HAITD-BOOK.  57 

Lbs.  in  a 
cubic  foot. 

Hickory   52 

Ebony   83 

Lignuin-vitae        -       -       -       -  83 

Pine,  yellow     -       -       -    .  .  38 

Cork     ......  15 

Pine,  white       -       -       -       -  25 

Bircli  charcoal      -       -       -       -  34 

Pine        "...       -  18 

Beeswax   60 

"Water  -      -      -      -  62^ 


i 

i 
i 


